I would say absolutely yes. That's 5.3 gallons per plant, which is plenty for those crops.

Just for reference, I regularly plant cucumbers (straight 8 is my favorite) at the rate of 1.5-2 gallons per plant. Every year I get all the cucumbers I can use, and then some. This year I plan on putting 4 cukes in a 6.5 gallon square planter with a tomato cage in the middle.

As for peppers, they thrive at 2 gallons per plant from my experience, and they enjoy being a little crowded (sort of like herbs). I know some people disagree with that, but last summer I planted 4 California Wonders in a 5 gallon bucket (which is only 1.25 gallons per plant) and I got about 25 peppers on them (and that is with poor, cheap soil).

The setup you describe is definitely enough for them to thrive.

Check out the photos of the planters I use for cucumbers in my blog I linked below. I get plenty of cucumbers by planting 4 plants per square deck planter (pictured) and you plan on putting 4 in a container roughly 5 times the volume of what I use.